Real time aperture photometry with Cherenkov telescope array

(1)

Alma Mater Studiorum

_{· Universit`}

a di Bologna

Dipartimento di Fisica e Astronomia

Corso di Laurea magistrale in Astrofisica e Cosmologia

Real time aperture photometry with

Cherenkov Telescope Array

Tesi di Laurea

Presentata da:

Simone Tampieri

Prof. Cristian Vignali

Relatore:

Correlatori:

Dott. Andrea Bulgarelli

Dott.ssa Valentina Fioretti

Sessione IV

(2)

(3)

(4)

(5)

Sommario

Il lavoro svolto nella mia tesi riguarda l’analisi del segnale proveniente da sor-genti gamma utilizzando la fotometria d’apertura in un contesto di analisi in tempo reale (i.e. Real-Time Analysis, RTA) effettuata con il Cherenkov Tele-scope Array (CTA). CTA è l’osservatorio di nuova generazione per l’astrofisica nei raggi gamma che fornirà una miglior comprensione dei fenomeni riscontra-bili nelle parti più energetiche dello spettro elettromagnetico con una sensibilità dieci volte migliore dei sistemi attualmente disponibili.

La mia tesi si concentra sulla valutazione della significatività del segnale nell’ambito del sistema RTA, una serie di processi dove un software valuta l’osservazione in tempi molto brevi e fornisce notifiche scientifiche quando ven-gono individuati fenomeni transienti nel campo di vista. La RTA si occuperà di analisi su osservazioni da pochi secondi a 30 minuti, cercando eventi tran-sienti ed avendo la possibilità di cambiare la strategia osservativa in corso e la programmazione della stessa. Un requisito centrale di RTA è la capacità di generare un’allerta scientifica entro 30 secondi dall’acquisizione del dato, quindi l’esecuzione delle mie analisi ha bisogno di rispettare questo vincolo.

Uno dei temi principali di questo lavoro `e definire il tempo minimo neces-sario per rivelare un fenomeno transiente come un Gamma-Ray Burst (GRB). Inoltre potranno essere fornite ulteriori informazioni riguardanti la sorgente in-dividuata, come una stima del flusso gamma e una curva di luce.

Individuare fotoni ad energie molto alte con esposizioni brevi, come 100 se-condi o meno, significa operare con conteggi scarsi sia dalla sorgente che dal background; per questa ragione `e stato effettuato un confronto fra i risultati ottenuti utilizzando l’analisi di massima verosimiglianza e quelli derivanti dalla fotometria d’apertura.

Per questo tipo di analisi sono stati considerati strumenti già esistenti per le consuete osservazioni su tempi lunghi ed uno in particolare è stato investigato. I risultati del confronto sono evidenziati nella tesi. Tuttavia, considerando i requisiti di RTA, durante l’evoluzione di questo lavoro è emersa la necessità di un approccio differente rispetto all’analisi di verosimiglianza sul campo di vista ed è stata sviluppata una tecnica innovativa basata sulla fotometria d’apertura. Il metodo per valutare il segnale su osservazioni in tempi brevi, come investi-gato nel mio lavoro, è cruciale nella generazione delle notifiche scientifiche e nelle attività derivanti dalle segnalazioni esterne di transienti (come i follow-up delle onde gravitazionali), e richiede una rapida estrazione del segnale e valutazione della rilevazione rispetto alla maggioranza degli studi che usualmente vengono effettuati con dati acquisiti su osservazioni della durata di diverse ore.

Il software in cui viene implementata la fotometria d’apertura per RTA ha dimostrato di essere accurato come altri metodi ma più flessibile, di fornire diverse misure utili (come i conteggi nella regione della sorgente e nel back-ground, oppure l’eccesso stimato), di poter generare metriche importanti (come la significatività della rilevazione o il flusso) in tempi più brevi. Inoltre sono stati identificati alcuni criteri per configurare il processo RTA in modo da individuare sorgenti simili a quelle simulate, fra cui l’afterglow di un GRB.

(7)

La mia tesi si sviluppa come segue:

• Il primo capitolo vuole presentare una panoramica dell’Universo alle alte energie, delle tecniche di Imaging Cherenkov e degli osservatori di raggi gamma, compreso CTA. In questo capitolo viene descritta anche l’RTA. • Il secondo capitolo descrive gli aspetti teorici e pratici coinvolti nell’analisi

dei raggi gamma, con interesse particolare verso l’analisi fotometrica di apertura che `e la metodologia principale del mio lavoro.

• La terza parte esamina brevemente ctools, un pacchetto software usato per analisi scientifiche nei raggi gamma. Questo software `e stato svilup-pato specificatamente per i dati di CTA, ma `e utilizzabile anche per altri telescopi ad Imaging Cherenkov come H.E.S.S., MAGIC o VERITAS. • Il quarto capitolo illustra i risultati ottenuti con l’analisi on/off effettuata

con ctools e con altre valutazioni fotometriche.

• Il quinto capitolo entra nei dettagli della tecnica innovativa sviluppata nell’ambito di questa tesi, sfruttando la fotometria d’apertura nei raggi gamma. Vengono mostrati i risultati ottenuti.

• Infine le conclusioni, dove viene presentato un breve riepilogo del lavoro svolto e sono indicate alcune idee per sviluppi futuri.

(8)

Abstract

The work accomplished in my thesis concerns the aperture photometry analysis applied to γ-ray source signal evaluation in the context of Real-Time Analysis (RTA) exploiting the Cherenkov Telescope Array (CTA) facility. CTA is the next generation γ-ray ground-based observatory which will provide a deeper understanding of the most energetic part of the electromagnetic spectrum with unprecedented sensitivity, a factor of ∼ 10 better then current facilities.

My thesis is focused on the evaluation of the significance of the signal through the RTA system, a specific pipeline where a software evaluates the observation in short time and provides science alerts when transient phenomena are de-tected in the field of view. The RTA timescales span from a few seconds to 30 minutes, searching for transient events and opening to a possible change of the observational strategy and schedule. An important requirement of the RTA is to be able to generate scientific alerts within 30 seconds with respect to the data acquisition, therefore my analysis needs to respect this constraint strictly.

One of the main topics of this work is defining the minimum time needed to detect a transient phemenon as Gamma-Ray Burst (GRB). Furthermore, additional information about the detected object will be provided, such as the γ-ray source flux measurement and lightcurve.

To detect very high-energy photons in short exposure as 100 seconds or less involves low counts from source and background; in this regard, a comparison between the best fit obtained using the maximum likelihood method and the one from aperture photometry was performed.

Existing tools for standard long-time analysis have been considered and one in particular has been tested. Results of this comparison are provided in my thesis. However, considering the requirements of the RTA pipeline, the neces-sity of a different approach with respect to the full field maximum likelihood has emerged and a novel technique, based on aperture photometry, has been developed and is described in this work.

The method to evaluate signals on short time scales – as pursued in my work – is crucial in alerts generation context and transient follow-up activities, but it requires fast signal extraction and detection evaluation compared to the large majority of studies usually developed on data acquired over long observation time (i.e. hours).

The RTA aperture photometry tool has proven to be as accurate as other methods but more flexible, producing multiple useful measures (i.e. on- and off-source counts, estimated excess), and capable of providing important metrics, as detection significance and flux, with a faster response.

In addition, sets of constraints have been found to configurate the RTA pipeline so that it can detect targets similar to the simulated GRB afterglow.

The outline of my thesis is the following:

• The first chapter is an introduction to very high energy Universe, to the Imaging Cherenkov Technique and γ-ray observatories – among which

(9)

CTA. The RTA will also be described.

• The second chapter describes the theoretical and pratical aspects involved in the γ-ray analysis, focusing on the aperture photometry analysis that is the main topic of my work.

• The third part examines briefly ctools, a software package used for sci-entific γ-rays analaysis — for CTA data, but also other existing Imaging Air Cherenkov Telescopes (such as H.E.S.S., MAGIC or VERITAS). • The fourth chapter illustrates the results obtained with the on/off analysis

via ctools and other photometric evaluations.

• The fifth chapter details a novel technique developed in this work based on aperture photometry for γ-rays. The achieved results are reported. • Finally the conclusions, where I will make a brief summary of the work

(10)

1 Gamma-rays in multimessenger era

Starting with visible light, astronomers studied the sky since ancient times. With time the astronomers have not only improved the observation tools, but they also grasped the most profound nature of the “light messenger” unfolding the electromagnetic radiation.

Although the electromagnetic radiation is a continuous and describes the full range of existent light, astronomers provided names for different regions of the spectrum: starting from low energy radio waves and microwaves, going through infrared, visible and ultraviolet light, up to the X-rays and, finally, γ-rays. The electromagnetic radiation unfolds over twenty orders of magnitude in energy, and the different energies allow us to analyze several emitting physics processes. Taking into account that the boundaries of the energy regions are blurred, we can consider photons with energy in the order of MeVs or greater as γ-rays photons. From this remarkable lower limit, γ-rays are categorized in “high en-ergy” when their energy is between 30 MeV and 30 GeV and “very high enen-ergy” (VHE) for those that exceed 30 GeV and grow up to the TeV. Sometimes the term “ultra high energy” is used to indicate those in the 30 TeV − 30 PeV interval.

It is worth noting that most of the light we receive is emitted by hot objects and is known as thermal radiation, but no object can become hot enough to emit at γ-rays frequencies. Indeed, the photons in the γ-ray band represent the most energetic photons of the electromagnetic spectrum and they are products of fundamental physics happenings in the more violent processes in the Uni-verse. Gamma-ray emission has been detected by pulsar, supernova remnants, relativistic jets from active galactic nuclei and so on.

To explore the γ-ray window provides an extraordinary picture of the non-thermal Universe and of the most spectacular events in the Cosmos.

On August 17th, 2017, a gravitational wave signal associated with the merger of two neutron stars was detected by LIGO and Virgo interferometers. The col-lision produced a simultaneous gravitational radiation (GW170817) and a short gamma-ray burst (GRB170817A), whose subsequent electromagnetic emissions were followed by 70 observatories in all the continents and in the space and opening a new era for the astronomy: the multimessenger era.

Nowadays astronomers are improving their understanding of the Universe not only exploring the full electromagnetic spectrum, but also investigating the elusive neutrinos from galaxies with exceptional rate of star formation or the faint gravitational waves emitted from collapsing binary systems. The γ-rays are perfect companions of all these fascinating events and to get information from all these complementary experimental branches is the key to obtain a complete knowledge of sources and environments in this multimessenger era.

1.1 The Gamma-ray Universe

Studying γ-rays means exploring the non-thermal Universe and violent phenom-ena in our Galaxy and beyond.

(11)

Somewhere in the Universe protons and atomic nuclei are accelerated to extraordinary high energies and, traveling very close to the speed of light, they bomb continuously the solar system. The energy of these charged particles, called cosmic rays1

(CRs), has been increased beyond the thermal energies by the surrounding astrophysical environments.

The energy spectrum of CRs cover a very wide range of energies, and follows a power law dN/dE ∼ E−Γ

with different spectral indices: a first transition point is the knee at E ∼ 3 · 1015_{eV, where Γ changes from 2.7 to 3. After}

this first change, the spectral index becomes harder at 3.3 around E ∼ 1017_eV.

Finally, a last transition called ankle flattens the spectrum with a 2.6 index at energy above 5 · 1018_{eV. The spectrum of CRs from different experiments is}

shown in Figure 1. Very energetic CRs have been detected with E ∼ 1020_eV,

far beyond energies achievable by the most modern particle accelerators on Earth.

Figure 1: Cosmic-ray spectrum measured by different experiments. In the y-axis the differential flux of particles per unit energy interval F (E), multiplied by energy E2.6_{, is reported. The knee and ankle are evident. Image from “Cosmic}

Rays” from [16].

The origin of CRs is still under debate, but they can have galactic and

1

The word ray is used for historical reasons. In 1912, V. Hess discovered a ionizing radiation originated in outer space. In 1926, R. Millikan named this radiation “Cosmic rays” thinking they were gamma rays at higher energy.

(12)

extra-galactic nature. Galactic CRs (energy up to 1015_{eV) are assumed to}

be accelerated in supernova remnants, while active galactic nuclei, gamma ray bursts, quasars are potential sources for extragalactic CRs. On the one hand, as charged particles, CRs are affected by magnetic fields encountered in their path, so they cannot be tracked back to their source. On the other hand, γ rays (and neutrinos) are neutral particles and can be produced in the same non-thermal phenomena that origin the CRs.

Unlike the sky in the optical energy range, the γ-sky is dominated by dif-fuse background radiations. An intense Galactic component is originated by charged particles propagating in interstellar medium and emitting γ photons via π0_{-decay, inverse Compton scattering and bremsstrahlung. An}

extragalac-tic background component represents the entire light emitted by stars, galaxies and active galactic nuclei over the full lifetime of the Universe. This extragalac-tic component will be described at the end of this section. In this background radiation, steady sources and flashes can be observed.

The Milky Way center contains several objects that could emit CRs and γ-rays. The main candidate surely is the supermassive black hole Sgr A* hosted in the Galactic Center. It is believed to emit γ-ray photons through the π0_-decay

(π0

→ 2γ) produced in hadronic interactions where relativistic protons and nu-clei collide producing pions, kaons and hyperons. This very high energy emission has been observed by different experiments in the Galactic Center direction but the origin is hard to track because the area is source-crowded. Recent measure-ments [29] interpretate the VHE emissions as the energy loss by high-energy electrons and positrons from many pulsars located near the Galactic Center. These charged particles can generate VHE photons via synchrotron radiation when they move through magnetic fields at relativistic speed or via inverse-Compton (IC) scattering when electrons lose energy in high density photon environments. The inverse-Compton scattering and the π0

-decay are believed to be the most important mechanisms to generate VHE γ-rays. Investigating ar-eas where π0_{-decay is dominant could lead to discovery of hadronic accelerators}

where CRs originate.

At the moment, in agreement to the TeVCat2

, pulsars and pulsar wind nebulae are the most represented galactic object emitting γ-rays at GeV and TeV energies. Pulsars (PSRs) are rotating neutron stars. If associated with an extended nebula, pulsars are classified as pulsar wind nebulae (PWNe). Both types can emit high-energy radiation, but the winds of energetic particles in PWNe are well suited to provide very high-energy γ-rays via inverse Compton effect of electrons on low-energy radiations. The most famous source of this type is the Crab Nebula, a pulsar born from a supernova explosion detected in 1054 AD and surrounded by the remnants of the progenitor star. The Crab is well-studied in all the wavelength (Figure 2) and in 2019 has been seen emitting photons with energy above 100 TeV [32].

When a massive star at the end of its life cannot oppose its internal pressure

2

TeVCat is an online catalog for TeV Astronomy by S. Wakely and D. Horan from the University of Chicago. See http://tevcat.uchicago.edu/ .

(13)

Figure 2: Multiwavelength observations of the Crab nebula. The synchrotron emission is given by the superposition of the contributions of electrons with different energies. The synchrotron spectrum provides the target photons for the inverse Compton process. Credits to M. Spurio [31].

to the gravitational forces anymore, it collapses and a Type II supernova explo-sion occurs. During the exploexplo-sion the most external materials of the star are ejected at thousands of kilometers per second and the shockwave heats the in-terstellar medium creating an expanding shell of gas and dust called supernova remnant (SNR). SNRs contribute to enrich interstellar medium with heavier elements and can play a role in star formation processes. Furthermore, galactic CRs are believed to be accelerated from the shock. The study of some super-nova remnants indicates that the γ-ray emission is consistent with the hadronic model [13], [19], but other contributions by the leptonic component (i.e. the bremsstrahlung process and inverse-Compton scattering) may increase the de-tectable flux of very high-energy photons and are debated [20], [25].

In our exploration of the Galaxy, the γ-ray binary systems have proven to accelerate particles up to very high energies. These objects have been deeply studied at X-ray wavelengths, but they populate also the γ-sky — indeed, a handful of these sources has been detected from H.E.S.S. and M.A.G.I.C. tele-scopes as described in [9] and [10]. When matter falls from companion to com-pact object a large amount of energy is released. The γ-ray spectrum to several TeV implies that the electrons and protons parent particles might be accelerated (e.g. via shocks) in accretion disks and jets and emit via synchrotron radiation or scattering abundant thermal photons to higher energy via Inverse Compton.

(14)

Another VHE emission scenario in binary systems occurs when a pulsar loses rotational energy via a relativistic wind composed by high-energy electrons in-teracting with surrounding plasma (see [3]). In this case Compton scattering, synchrotron radiation and π0

-decay mechanisms are involved.

Accretion disks have a critical role in very energetic emissions from extra galactic objects: the Active Galactic Nuclei (AGN). The active galaxies are characterized by supermassive black hole (SMBH) collecting matter from the surroundings. The falling matter is strongly heated in the inner parts of the accretion disk near the SMBH and radiates at optical and ultraviolet frequencies via dissipative processes, up to X-rays energies when very energetic electrons interact with photons from the very hot corona region where inverse-Compton phenomena occur. Some AGN can have a nonthermal emission when highly energetic particles are accelerated in relativistic jets of plasma that may form perpendicularly to the galaxy plane when the black hole spins and the accretion disk is strongly magnetized [33]. These jets can accelerate particles as protons up to PeV energies3_{, so they can contribute to CRs generation and initiate pair}

cascades that can radiate synchrotron γ-rays in the high-energy regime [28]. A few times per day the γ-ray sky is characterized by extremely luminous eruptions called gamma ray bursts (GRBs) that exceed the γ-ray emission from any other source. These flashes are randomly distributed in sky directions and it is currently known that they have an extragalactic origin. GRBs are the most energetic phenomena in the Universe, and were discovered serendipitously in 19674 _{and publicly announced in 1973. The bursts are featured by amazing}

energy release (∼ 1052 _erg5_{) in very short time, and they are mainly classified}

in short-duration (from few milliseconds to about 2 seconds) and long-duration bursts (up to hundreds of seconds) — see Figure 3. Ultra-long GRBs, emitting continuously for thousands of seconds, are also under study.

With the discoveries of the Italian-Dutch BeppoSAX mission, launched in 1996, GRBs have been also characterized by a post-prompt afterglow phase. This phase lasts more than the prompt one (the typical duration time is one week) and the spectrum is distributed through all the wavelengths: indeed, the study of the afterglow emission in multi-wavelength observations was important to determinate the events’ redshift and the possible origin of the main γ-ray emis-sion.

Observations have shown that long GRBs appear where active star forming galaxies are, and a correlation with supernova events has been found in many cases [15]. The short GRB population has a higher energy spectrum than longer GRBs by many orders of magnitude and their presence has been confirmed in galaxies containing a considerable quantity of old stars compatible with neutron

3

The origin of ultrahigh energy CRs is still not clear, but shocks in the backflows of radio galaxies can meet the physical requirements to accelerate particles up to the EeV regimes [35].

4

During the Cold Wars years, USA and USSR launched military satellites to monitor nuclear weapon explosions that violated nuclear test ban treaty. In July, 1967 the U.S. Vela satellites identified suspicious gamma emissions to which a cosmic origin was attributed.

5

As a comparison, the estimated luminosity of the Milky Way is 1043

erg/s. The Sun provides 1033

(15)

Figure 3: Durations of the 4B Catalog Gamma-Ray Bursts recorded with the Burst and Transient Source Experiment on board of NASA’s Compton Gamma-Ray Observatory. The duration parameter used is T90, which is the time over which a burst emits from 5% to 95% of its total measured counts. The data used for the calculation are the BATSE 4 energy chan-nel discriminator data. Lightcurves used for the calculation of T90 are inte-grated over all 4 channels (E > 20 keV). Image from BATSE group here https://gammaray.nsstc.nasa.gov/batse/grb/duration.

stars binary systems. The current hyphotesis is that short GRBs are generated from processes where two compact objects merge: when a couple of neutron stars spirals closer, in the very last moments the structure emits gravitational radiation, thermal neutrinos, and an amazing quantity of energy.

The most accredited acceleration mechanism producing γ-rays is the fireball

model (see Figure 4) and is independent on the details of the region where it

is originated. In agreement to this model, the photon emission starts with an energy release where the radiation pressure overcomes the gravity, causing an explosion of relativistic blast waves. These pressures generate different shells of progenitor matter, each moving at its own speed: when a fast shell encounters a slower one an internal shock happens and the GRB prompt emission is emitted. While shells interact with the interstellar medium, external shocks produce the GRB afterglow.

The Universe is permeated by diffuse radiation fields present at all wave-lengths. The most well known radiative background is surely the Cosmic

(16)

Mi-Figure 4: Production sites of γ-ray and afterglow emission in the fireball model. Progenitor models for short and long GRBs are shown on the left. Image from [18].

crowave Background (CMB) that provides information about the very early Universe and dominates at longer wavelengths. The total light emitted by stars, galaxies and AGN in all the epochs is a pervasive background radiation spanning from ultraviolet to infrared frequencies and it is called Extragalactic Background Light (EBL). When a very high energy photon travels through the intergalactic medium, the interaction between it and an EBL photon will lead to the pair creation γ + γbackground → e++ e− and to the absorption of the very high

en-ergy extragalactic photon. The interaction is dependent on the EBL’s spectral energy distribution and the redshift of the γ-ray source. Direct measurements of EBL are hard to take and a wide range of models has been developed (see, for instance, Finke et al. 2010 [14], Gilmore et al. 2012 [17]).

1.2 The Imaging Cherenkov Technique

The Earth’s atmosphere is opaque to γ-rays: when a very high energy photon interacts with the atmosphere it produces electron/positron pairs (Figure 5). These secondary particles provide new secondary γ-rays via a bremsstrahlung mechanism that emits pairs again, creating an electromagnetic cascade with a so-called “shower effect”6_{. A great number of these particles travel with}

relativistic speed through the atmosphere generating Cherenkov light — a de-tectable near-UV radiation flash at 300–350nm. When a charged particle tra-verses a medium with a speed larger than light speed in that medium, Cherenkov light is emitted. Conversely to optical telescopes, the Cherenkov telescopes do not look at celestial objects, but record nuclear reactions in the atmosphere

6

As historical note, the term “shower” is the English translation by P. Blackett of the Italian expression “sciame”, first used by B. Rossi (citing [31]).

(17)

following the Cherenkov flashes that accompany them.

Figure 5: Image explaining how CTA detects Cherenkov light produced by a primary γ-ray interacting with the Earth’s atmosphere. Credits to https://www.cta-observatory.org.

When high-energy γ photons and CRs impinge the Earth’s atmosphere, the interactions with atmospheric nuclei create secondary particles that induct the shower. The shower creation persists until a specific energy threshold7_{is reached}

and the maximum number of shower particles was produced. This maximum emission occurs at an altitude of about 10 km above the sea level for primary particles in the 100 GeV–10 TeV energy range.

An electromagnetic cascade (containing e+

, e−

and γ-rays) propagates Che-renkov light as a cone with a maximum emission angle θC= cos−1(1/n) ≈ 1.3◦

at standard temperature and pressure (STP) conditions. The angle increases going from top to ground level following the atmosphere’s refraction index n that changes with altitude. An electromagnetic shower can propagate for 10 km re-sulting in a projected light pool with about 120 meters radius at ground level (about 2000 meters on sea level). The Imaging Atmospheric Cherenkov Tele-scopes (IACTs) use wide-field mirrors to focus the light pool towards high-speed cameras to detect nanoseconds-lasting faint Cherenkov flashes.

7

The energy at which radiation energy losses equal those derived from excitation/ioniza-tion. This energy depends on the medium refraction index, therefore can change at different altitudes.

(18)

The shower image, an approximately elliptical shape on the camera, is an-alyzed in an early phase to reconstruct the primary γ-ray origin, energy and direction. The electromagnetic showers, like those initiated by γ-rays, are dif-ferent from the hadronic showers initiated by CRs (protons and nuclei). The former showers project compact elliptic shapes on the focal plane, while the latter have larger structure deriving by π0

decay and can be therefore distin-guished. The air showers initiated by electrons/positrons8

constitute irriducible isotropic background for IACT detectors because they have the same develop-ment as those deriving by γ-ray photons.

The efficiency in discriminating between hadronic and γ-ray showers defines, among other parameters, the minimum detectable flux (the sensitivity) of the telescope.

After raw data are collected, an image cleaning process occurs to reconstruct the shower information needed to perform the parametrization of the shower itself.

The fundamental image parameters were introduced by A. M. Hillas [5] in 1985, when single telescope configuration was still used. Through these param-eters it is possibile to evaluate the obtained Cherenkov images and achieve a good γ-ray/hadron separation.

• SIZE is the total number of photoelectrons in the shower image. It is proportional to the energy of the incoming primary γ-ray or particle; • LENGTH is the half of the major axis of the shower image;

• WIDTH is the half of the minor axis of the shower image; • FRAC measures the general concentration of light;

• MISS is the perpendicular distance of the center of the field (where the source is supposed to be in single telescope configuration and pointing in center of field of view) from the image axis;

• AZIMUTHAL-WIDTH is the image width relative to a new axis which joins the center of the field to the centroid of the image;

• DISTANCE is the distance of the brightest point from the center of the field.

Through these parameters (Figure 6), Hillas noticed hadronic showers had wider images, not systematically aligned with the source because isotropic, while γ-ray showers were more collimated.

When the source is not in the camera center (i.e. the telescope is pointing in Wobble mode, see section 2.5), new useful parameters are used to track the source position:

8

(19)

Figure 6: Parametrization of a shower image through Hillas parameters. The nominal position of the observed source is (x0, y0). The full parameters

descrip-tion is provided in the main text. Credits to [22].

• ALPHA is the angle between the major axis of the ellipse and the direction of the source position from the center of gravity of the image;

• DIST is the distance of the center of gravity of the image from the source position.

The ALPHA parameter has the highest γ-hadron separation power since γ-ray images have small values, while hadron images have flat distributed AL-PHA angles.

Observations of individual showers with array of Cherenkov telescopes al-lows a three-dimensional reconstruction of γ-ray showers in a more effective stereoscopic observation9_{. Reconstruction algorithms are used to point back to}

the astrophysical source and to discriminate the electromagnetic showers from

9

Quoting [31], the stereo observation increase the background suppression efficiency by a factor about 100, improves the angular resolution and enable morphological studies of extended γ-ray sources.

(20)

the hadronic showers produced by isotropic cosmics rays. These algorithms are based on Hillas’ parameters and are implemented with statistical techniques like the Random Forest regression method [12].

After this step, the reconstructed data can be collected and processed to provide science results.

1.3 Previous very high-energy experiments

Gamma-ray signals have been studied in various ways over the time since the 1960s: using balloons, water ground-based detectors, imaging ground-based tele-scopes and detectors on spacecraft.

In the sixties γ-ray emissions were detected by instruments on satellites (Vela, OSO3) but the first detailed sky map were took in the seventies with SAS-2 and Cos-B satellite missions. The resolution of these instruments was insufficient to detect most of γ-ray point sources, but they recorded the diffuse Galactic emission due to the interactions of CRs with the interstellar medium, some pulsars and unidentified objects10

.

In the 90’s two important satellites took off: the Compton Gamma Ray Observatory (CGRO) and BeppoSAX. CGRO carried different instruments for specific gamma-ray astronomy: among them, the Burst and Transient Source Experiment (BATSE) contribution was remarkable as it led to the detection of one GRB per day (for about 2700 total detections). The Energetic Gamma Ray Experiment Telescope (EGRET) was the high-energy instrument on CGRO, covering the energy range from 20 MeV to 30 GeV, and it conducted the first survey above 100 MeV. BeppoSAX identified the first non-gamma ray counter-part to a GRB, opening the way to a better characterization of GRBs and their extragalactic distance. These space missions were followed in 2000s by Swift, INTEGRAL, Fermi and AGILE that contributed to map the γ-ray emissions from pulsars, GRBs, microquasars, black holes and background radiation.

Recent space experiments cover a γ-ray energy interval from a few MeV to hundreds of GeV. However, beyond the GeV range the γ-ray fluxes are so small that the effective detection area of space-based experiments cannot provide a sufficiently large collection of events, so the astrophysics studies rely on ground-based detectors11_.

Starting with the Whipple Telescope in Massachussets in 1968, the ground-based telescopes have grown in number and technologies. The Imaging Air Cherenkov Technique was developed in the 70s, just with the Whipple tele-scope; since then the field has been demonstrated to provide contributions in astrophysical observations and particle physics. In the last two decades ground-based gamma-ray astronomy has experienced impressive astrophysical results obtained with facilities like H.E.S.S., VERITAS and MAGIC. A short summary is in Table 1.

10

One of the best known results of Cos-B is the 2CG catalogue with 25 γ-ray point sources discovered in three years. See https://sci.esa.int/s/8OpVjpA .

11

The Fermi effective collecting area is ∼ 6500 cm2

(21)

The High Energy Stereoscopic System (H.E.S.S.) has a five telescope con-figuration (four 12 meters in diameter mirrors, with a larger 28 meters mirror built in the center of array) which allows to investigate γ-ray sources in the energy range from 10s GeV to tens of TeV with intensities much lower than the Crab Nebula flux. H.E.S.S. is operative in Namibia since 2002 and was updated in 2012 with the 28 meter mirror. Over time it has detected several TeV γ-ray sources and reported the presence of petaelectronvolt protons from the supermassive black hole at the Milky Way center [26] in 2016.

The Very Energetic Radiation Imaging Telescope Array System (VERI-TAS) is another ground-based γ-ray observatory with a peak effective area of 100,000 m2 _{to receive signals from very high energy band. VERITAS was}

de-signed on the Whipple project (decommissioned in 2013) and was originally planned as an array of seven telescopes, but only four were built. In 2009, one telescope was moved to a new location to improve the system sensitivity. The VERITAS telescopes are able to slew simultaneously at a rate of 1◦

per second in elevation and azimuth enabling the GRB observations. Since 2008, VER-ITAS has discovered new TeV sources and allowed to study SNRs and Crab Nebula deeply. Furthermore, it has observed over one hundred AGN and it has an extensive Dark Matter program.

The Major Atmospheric Gamma-ray Imaging Cherenkov (MAGIC) is a two-mirror Cherenkov telescope with a very fast repositioning (7 degrees per second) of about 40 seconds on average in order to quickly react to alert for transient events like GRBs. The dish of both telescopes has a 17 meters diameter and they were installed on Canary island of La Palma in 2004 and 2009. More technical and performance information are described in [24]. Until the advent of the CTA observatory, MAGIC is the most advanced Cherenkov telescope for gamma astronomy.

Instrument Emisph. Alt. no. FoV ang. res. slewing energy range tel. at 1 TeV time (s)

Whipple North 2300 1 2.6 0.12 180 300GeV–10TeV H.E.S.S. South 1800 4 5.0 0.1 n/a 30GeV–100TeV H.E.S.S. II South 1800 1 3.2 0.4 61 30GeV–100TeV

VERITAS North 1275 4 3.5 0.08 100 85GeV–30TeV

MAGIC North 2230 2 3.5 0.07 40 30GeV–100TeV

Table 1: Summary of Cherenkov observatories. The altitude is in meters, field of view in degrees. The slewing time is intended as an approximation. In-formation about these telescopes are eterogeneous given the composite nature of these detectors systems. Whipple project is showed for historical reason (it was decommissioned in 2013). Furthermore, many facilities have been updated changing initial characteristics: Whipple has improved its angular resolution from initial 0.3 degree, HESS installed a new mirror (H.E.S.S. II) and the NEC-TAr faster chips, and so on.

(22)

1.4 The CTA observatory

The Cherenkov Telescope Array represents the state of the art for the γ-ray detections at ultra-high energy. This ground-based telescope will bring a signif-icant improvement in terms of accuracy and sensitivities in the γ-ray astronomy and a broader than ever observable energy interval — from tens of GeV to the hundreds of TeVs.

CTA will be composed with more than 100 telescopes: about 19 in the north-ern emisphere, in La Palma island, and 99 telescopes in the southnorth-ern emisphere in the Atacama Desert in Chile. The northern site array, with large and medium size telescopes spread in about 0.5 km2_{area, will focus on low-mid energy range,}

from 20 GeV to 20 TeV. The southern site array will cover energies from 20 GeV up to 300 TeV with the full range of telescopes (small, medium and large sized) built in about 5 km2

area in Paranal.

The CTA telescopes are from three different classes, each covering a specific energy range. The Table 2 is a short summary about the different classes of CTA telescopes.

Instrument number of FoV ang. res. slewing energy range

telescopes at 1 TeV time (s)

LST 4N + 4S 4.5 n/a 30 20GeV–150GeV MST 15N + 25S 8.0 n/a 90 150GeV–5TeV SST 0N + 70S 10.0 n/a 60 5TeV–300TeV North or South 0.05 20GeV–300GeV full array

Table 2: CTA telescopes summary. The field of view is reported in degrees. The angular resolution is given only for a full array configuration and not for telescope’s size.

At the center of the northern and southern sites a set of 4 large-sized tele-scopes (LST) will rise to catch the fainter Cherenkov lights from the low-energy gamma rays (20-200 GeV) with a 4.5 degrees field of view. The large tele-scopes are amazing instruments that can re-position their 400 m2

mirror with a 28-meters focal in tens of seconds to allow quick follow-ups of transient (i.e. GRBs) alerts. The first LST prototype, LST-1, was completed at La Palma, Ca-nary Islands, in October 2018 and detected its first γ-ray signal on 23 November 2019 pointing the Crab Nebula12_.

About 40 medium-sized telescopes (MST) will be in the array, covering 100 GeV–10 TeV energies. The MSTs will be placed in both the emispheres and scattered around the large-sized telescopes and spaced about 100 meters from each other. The MST mirror is 12 meters in diameter with an 8 degrees field of view, useful for a rapid survey of γ-ray sky.

The small-sized telescopes (SSTs) will outnumber all the other detectors in an array with 70 units. The SSTs will be sensitive at the higher energies

12

(23)

Figure 7: The proposed layout for all the types of telescopes in the CTA project, in Northern (left) and Southern (right) sites. Credits to www.cta-observatory.com.

detecting γ-rays from a few TeVs up to hundreds of TeV with 4 meters in diameter mirrors13_{. Operating in the most extreme energy range (as 5 TeV–}

300 TeV) where the number of detected γ-rays showers will be rarer, SST array need to cover an area of several square kilometers.

The proposed layout for all the CTA telescopes is displayed in Figure 7. The current baseline design of CTA foresees a factor of 10 improvement in sensitivity in the current energy domain of about 100 GeV to some 10 TeV and an extension of the accessible energy range well below 100 GeV and above 100 TeV (see Figure 8).

The southern hemisphere array will cover the full energy range from tens of GeV to hundreds of TeV to allow a deep investigation of the central part of the Galactic plane and see most of the Galactic sources. Indeed, a key science project of CTA is the Galactic Plane Survey that will cover the entire Galactic plane looking for very high energy source population as PWNe, SNRs, and bi-naries [34]. The northern hemisphere array will be optimised for extragalactic astronomy, and will consist in the low-medium energy instrumentation (up to about 1 TeV). The EBL attenuation on TeV photons provides an effective hori-zon that makes sensitive instruments with low energy thresholds more suitable to detect distant objects.

The CTA Consortium, established in 2008, includes over 1300 members from 210 institutes in 32 countries in all the continents. Therefore, the CTA col-laboration can be defined as a world wide effort promoting a strong and true no-barrier cooperation.

13

One among SST prototypes is the italian ASTRI project, a dual-mirror Schwarzschild-Couder configuration that detected its first Cherenkov light in 2017, and achieved the first Crab detection in December 2018 [37].

(24)

Figure 8: Sensitivity curves of different very high-energy facilities. The CTA data are from the more recent public version prod3b-v2 IRFs. Credits to www.cta-observatory.com.

1.5 The Real-Time Analysis

The Real-Time Analysis (RTA) is a software system that analyzes CTA data while the observation is in progress. The scope of this software is to detect un-expected events and trigger science alerts when transient phenomena are identi-fied with specific time contraints. The RTA workflow must be operative during the observation to monitor the field of view for variability on a wide range of timescales and to provide scientific feedbacks that could change the observation strategies in live time.

To maximize the scientific return, the CTA observatory will have to be able to detect transient sources and to broadcast fast alerts with a latency of 30 sec-onds with respect to the last acquired event. It will search phenomena on dif-ferent timescales – from seconds to hours time windows – and with an analysis sensitivity not worse than a factor of 3 than the final one [21].

Thanks to its large sensitivity and fast slewing ability, CTA will play a crucial role in very high energy counterparts searches in gravitational wave and neutrino follow-ups. The key science projects which rely on the short-timescale capabilites of CTA include transients as GRBs and PWN flares, flaring activities by AGN, and variable objects as γ-ray binaries on the Galactic Plane.

The RTA requires effective systems communications with strict time con-straints, speed and accuracy in analysis process which should last between 10 seconds to 30 minutes, but also a flexibile strategy to detect different types of

(25)

transient phenomena or serendipitous discoveries, and reliability — the expected RTA availability must be greater than 98%.

Figure 9: A gravitational wave follow-up program of CTA with the RTA pipeline. On the left side, the gravitational wave sky map with superimposed in purple the CTA pointings to inspect with RTA software is shown; this follows the algorithm on the right side of the figure. Modified from an original drawing by ICRC2019 [36].

In Figure 9 a gravitational waves follow-up is shown. After the gravitational waves detections, an array of positions to be verified will be evaluated by the CTA observation scheduler. A sequence of observations will be analyzed by the RTA software to identify the electromagnetic emission position corresponding to the gravitational signal. If no detection is localized, a new observation from the starting array is selected and analyzed. If RTA finds an electromagnetic signal in the chosen area, a second step begins and the RTA pipeline evaluates the γ-ray signal and stays on the same area following the electromagnetic transient until the flux has a satisfying significance. When the identified transient has faded, the specific observation is ended and the telescope returns to the original schedule preceeding the follow-up.

The RTA will be a key system in the messenger context and multi-wavelength astronomy and this software will be installed and run on-site, with the telescopes.

(26)

2 Analysis of Gamma-ray signals

In this chapter I will describe different aspects of signal analysis in the very high energy γ-rays context. Due to the astrophysical characteristics of the γ radiation and the features of the telescopes used to collect the signal, several techniques are used through various steps to provide reliable results.

When a high-energy photon, emitted by a γ-ray source, collides with the Earth’s atmosphere, the net result is an electromagnetic air shower that pro-duces Cherenkov emission then observed with an array of optical telescopes on the ground as described in section 1.2. The light generated in the shower triggers the telescope, and the incoming signals are cleaned and classified to reconstruct the primary event. Unfortunately, the observations are highly dominated by background events originated mainly by cosmic hadrons, therefore major effort is needed to discriminate astrophysics events and background. Finally, a list of reconstructed photons is provided and the high-level γ-ray analysis will be per-formed to evaluate the signal and to provide skymaps, spectra and lightcurves. Different approaches can be followed for this kind of analysis, and they will be described in the following sections.

2.1 The aperture photometry analysis

Measuring the photons received from astronomical sources is the main way to get information about the sources themselves. The aperture photometry is a technique to collect fundamental photometric qualities (as the number of pho-tons) from astronomical images in specific regions of interests. Starting from a photon list it is possible to estimate the source event counts applying the so-called on/off method. Conventionally, a closed region (the aperture) containing the source is centered on the source itself and used to count the on-source pho-tons Non. Unfortunately, this is not sufficient to evaluate the contribution of

photons by the source: a pervasive background needs to be removed from “be-hind” the object in the aperture. A background estimation is derived observing one (or more) off-source region with no source signals in. The number of pho-tons Nof f inside the off regions is the contribute from background apertures. If

it is desiderable to use many and large background regions to get good statistics, it is also important not to contaminate the data with background counts too different from those expected in the source one. Therefore background regions must have the same characteristics of the source region, as far as possible.

The excess photons from the source are calculated subtracting the normal-ized number of off regions events from the on-region data. The probable number of photons contributed by the source is:

NS = Non− αNof f (1)

where Non are the counts in the source region, Nof f are the entries in only

background regions and α is a background scale factor. To achieve a valid back-ground statistics, several observations are usually necessary, introducing more

(27)

scaling factors to consider, because the on and off observations are characterized by different effective area (A), and/or exposure (t) and/or size of the region (k):

α = Aon· ton· kon Aof f· tof f· kof f

. (2)

Having extracted the counts in the on and off regions and the excess counts, it is possible to estimate the detection significance, the source flux and the lightcurve with no modelling and in a simple and fast way.

2.2 The full field maximum likelihood analysis

Another popular method to analyze the data is the likelihood statistical tech-nique, used to quantify the relative extent to which the data support a statistical hypothesis [8]. The likelihood is the joint probability of the observed data given the hypothesis and can be used to estimate parameters through its maximization — hence the expression “maximum likelihood estimation”.

Likelihood analysis can be performed in binned or unbinned way, taking into account the number of events available for bin (e.g. pixels or time). For photon counting experiments, the binned likelihood that observed data are following a specific γ-rays emission model is given by the product of the probability for the finite number of i bins

L =Y i P (i) (3) where P (i) = θ ni i ni! e−θi ₍₄₎

is the Poisson probability of observing ni count when the predicted count by

model is θi. The logarithm of likelihood used to estimate the parameters is

ln L =X i niln θi− X i θi (5)

where the ni! from equation 4 is model independent therefore it is ignored, ni

is the number of observed events for each bin, and θi is the predicted number

of events from model14

.

When the number of events for bin is small, unbinned likelihood analysis is preferable. With a very fine mesh of bins, ni is either 0 or 1, and likelihood

becomes ln L =X i ln I(i|M) −X i θi (6)

where I(i|M) is the probability density of receiving a photon i at the point where one was received, given the model M .

14

It is worth noting that the first term in equation 5 increments the likelihood when dicted counts are where real counts actually occur, while the second term subtracts the pre-diction value dampening excessive assessments by the model.

(28)

The ratio between two likelihoods allows to compare the two models: in-deed, the likelihood ratio test is used to compare a null hypothesis for the data divided by the likelihood of alternative hypothesis for the same data. The like-lihood ratio test becomes particularly useful applying the fundamental Wilks’ theorem [1] that proves that the statistic distribution of the log-likelihood ratio

T S = −2 lnL_Lnull

alt

(7) when null hypothesis is true, is expected to asymptotically follow χ2

n−m, except

for terms of order N−1/2 _{where N is the number of samples and n − m is the}

number of degrees of freedoms. The parameter estimation via likelihood ratio in high-energy astronomy was performed by Cash in the late seventies [2].

A likelihood analysis on a full field of view offers the potential to reach great sensitivity and accurate flux measurement, as backgrounds can be modeled out and detailed source models can be applied.

2.3 Evaluating detections with Li & Ma significance

The procedures to analyze results in γ-ray astronomy experiments are examined in the 1983 Li and Ma article [4]. Particular attention is needed to determinate the confidence level of a candidate source, distinguishing an excess associated with a genuine source from background fluctuations and systematic effects that should have been removed.

Li and Ma show, through Monte Carlo simulations, that the significance based on standard deviation of the number of background photons (i.e. ˆNB =

αNof f), (a) does not follow a Poisson distribution if α 6= 1 when the significance

S = NS / pαNof f, and (b) underestimates the statistical error of the signal

and overestimates the significance when S = NS / αpNof f.

Furthermore, similar considerations are made for significance evaluated as S = NS/√Non and S = NS/√NS.

Therefore, Li and Ma solve the estimation of the significance issues with the likelihood ratio method.

Starting from equation 1 and using the Wilks’ theorem [1] to test the null hyphotesis that all the observed photons are due to background, Li and Ma define the maximum likelihood ratio as the rate of probability of null hyphotesis versus the alternative hyphotesis as follows.

The null hyphotesis has signal NS = 0 and extimated background counts as

NB= (α/(1 + α)) · (Non+ Nof f), so the likelihood function is:

Lnull= Pr Non, Nof f|hNSi = 0, hNBi = α 1 + α(Non+ Nof f) = Pr Non|hNoni = α 1 + α(Non+ Nof f) · Pr Nof f|hNof fi = 1 1 + α(Non+ Nof f) (8)

(29)

and the alternative hyphotesis function is:

Lalt= Pr(Non, Nof f|hNSi = Non− αNof f, hNBi = αNof f)

= Pr(Non|hNoni = Non) · Pr(Nof f|hNof fi = Nof f) .

(9) Developing the calculations from the two previous equations 8 and 9 with a Poissonian distribution

P (k) = n

k

k!e

−n ₍₁₀₎

where n is the expected number of events and k is the number of observed events, the resulting maximum likelihood ratio is:

λ = Lnull Lalt = α 1 + α Non+ Nof f Non Non 1 1 + α Non+ Nof f Nof f Nof f . (11)

In this case Li and Ma test the null hyphotesis with only one free parameter that is the expectation of the number of source photons hNSi.

According to the Wilks’ theorem, if the null hypothesis is true, −2 ln λ follows a χ2

1 distribution, and if u is a standard normal variable, u

2 _{will follow a χ}2 1, so we have: −2 ln λ ∼ χ2 (1) u2 ∼ χ2 (1)

from which the authors take the value (−2 ln λ)1/2_{as significance:}

S=√2 N_onln 1 + α α _N on N_on+ Nof f + Nof fln (1 + α) _N of f N_on+ Nof f 1/2 (12)

If an event was obtained by a single observation and Non and Nof f counts

are not too few, the value of significance is evaluated by equation 12. The probability that an event with a significance which is not less than S is produced by background can be evaluated with the standard Gaussian probability

p = N (u = S; µ = 0, var = 1) (13)

The article proves the equation 12 can be applied with fewer counts (Non ≥

10 and Nof f ≥ 10) and it is consistent with Gaussian probability and can be

applied also when α 6= 1.

2.4 The reflected-region background

The ground based very-high energy γ-ray telescopes have remarkable sensitivity but to achieve their full detecting potential they need to handle a main source of systematic error: the subtraction of background. The background estimation in γ-ray data analysis is a key element in Imaging Atmospheric Cherenkov tech-niques. In the low-level reconstruction phase it is mandatory to distinguish CR

(30)

induced hadronic showers by the γ-ray initiated showers. Later, in the high-level data science analysis, it is needed to evaluate the γ-ray signal from the science target. As described in § 2.1, to perform an aperture photometry analy-sis it is needed to count photons in on source region and subtract an estimated background.

Many background strategies can be adopted to estimate an observation back-ground [11], and the common goal is to provide the better estimation of the term αNof f from equation 1.

The reflected-region background model was originally developed for wobble observation (§ 2.5) where the source was not at the center of the field of view but displaced with an offset with respect to the telescope pointing direction. The simplest reflection estimation uses a single off region in the opposite direction relative to the center of the field, with the same shape of the on source region. To have a better statistics in the background measurements, the method can be generalized using a number of background regions equidistant from the telescope pointing direction (see Figure 10). Off regions near the one of the source are avoided to prevent the contamination by spilled counts from the on region.

Figure 10: Reflection algorithm with a 0.7 degrees angular distance between source and pointing direction.

(31)

The sum of the event counts Nof ffrom these off regions are used to estimate

the background of on region, scaled by an α factor – the number of off regions. This method cannot be used without an appropriate offset between pointing and source direction that avoids overlapping between regions.

2.5 The wobble method

In a typical observation the source is located at the center of field of view. To determinate the background counts, an analogue sky region must be observed with the possibility that the observational conditions may be different (clouds, humidity, lights, etc.). The background region is chosen in a such way that during the off observation the telescope tracks the same range of zenith angles as during the source tracking.

Furthermore, having to take these different pointings into account, the overall observation time will be splitted between pointings, reducing the crucial collect-ing time on the γ-ray emittcollect-ing source.

Exploiting the wide field of view typical for IACTs, the observations are of-ten performed in the so-called “wobble” mode, an observational strategy where the pointing of the telescope is slightly off-axis with respect to the source center under observation. Instead of observing the source at the center of the field of view, the telescope points with an offset with respect to the source position and extracts signal from the on region while the background counts will be ex-tracted from at least one false-source (or anti-source) region (see [7]) placed at a symmetrical position with respect to the pointing direction. The resulting distance between source and false-source regions is chosen in a way that back-ground measurement is not influenced by the source presence itself. Under such observation mode, the on and off regions are observed at the same time, making more efficient the limited duty cycle of these telescopes. The region radius is fixed during all the observation time. For extended sources, typically only a single off region is considered in order to avoid overlap of the on and off circles. Due to the alt-azimuth mount of the telescope, the on-source and false-source regions rotate around the center of the camera following the circumference of radius equal to the source-pointing distance. In Figure 11 two false sources are selected. In this case, the candidate γ-ray event rate for the source is the difference between the rate at the source position and the average rate at the two false source positions. The significance of the signal is

SN R = R − (F1+ F2)/2 [R + (F1+ F2)/4]1/2

(14) where R denotes the rate of gamma-ray showers at the source position and F1

and F2 denote the rate at the false source position [7].

This tracking mode captures photons spreading systematics errors and keep-ing the same observkeep-ing conditions for all the considered regions, thus increaskeep-ing the accuracy of cosmic-ray background. Moreover, this observation mode in-creases the available observation time while decreasing systematic differences

(32)

Figure 11: Movement of the real and the false sources in the field of view of the telescope in the tracking method when the telescope mount is altitude-azimuth. F is the false source, R is the real source, C is the center of the field of view. Solid lines are the movement trajectories. Original image from [7].

between on and off regions. The duration of the observation session is limited only by zenith angle and external conditions (i.e. weather). The wobble strategy involves a loss of sensitivity due to off-axis observation, but this is compensated by the possibility to observe the source continuously.

For the CTA’s Large Size Telescope inaugurated the October 10th, 2018 in La Palma, a wobble observation mode will be adopted. The LST-1 observation strategy will be the following: adopting a shift between pointing and source position between 0.4 and 0.8 degrees, the source position will be swapped of 90 degrees every 20 minutes, as illustrated in Figure 12. Then the procedure will take off counts from 3 fake regions in the same time of the source region, saving observation time and recording background counts at the same conditions. This pointing strategy will be used in the analyses described in § 5.

(33)

Figure 12: Wobble strategy for LST-1. Every 20 minutes the pointing direction swap by 90◦

with respect to the source region center, keeping the same distance. The souce region is displayed in green, the off regions are red. The pointing distance is between 0.4◦

and 0.8◦

(34)

3 The ctools framework

In this chapter ctools are described, the framework provided by Institut de Recherche en Astrophysique et Plan´etologie (IRAP) for the scientific analysis of CTA high-level data.

3.1 Introducing ctools

ctools is an open-source software framework developed by J. Kn¨odlseder et al. [27] to perform scientific analysis of astronomical data from Imaging Air Che-renkov Telescopes (IACTs). The ctools framework leverages on GammaLib, a powerful and flexible core library written in C++. Furthermore, many high-level ctoolsfunctionalities are wrapped and extended in Python language (i.e. the cscripts) to make the user interface easier and providing a better readibility to the not-technical users.

ctools provides ready-to-use programs to create and drill down datasets. Information and examples about this framework are available online15_and

doc-umented on published papers as [27].

The software is designed to analyze high-level data after the reconstruction phase (see § 1.2), so the simulated events have no information based on the air Cherenkov shower image characteristics but represent the reconstructed primary photons from source and diffuse background.

The ctools framework includes an instrument response functions (IRFs) database, required in many processes to take into account the instrument in-fluence during the observation. The IRFs describe the transformation from physical properties of photons to measured events and for CTA are factorized into effective area, point spread function and energy dispersion as

R(p′ , E′ , t′ |p, E, t) = Aef f(p, E, t) × P SF (p ′ |p, E, t) × Edisp(E ′ |p, E, t) . (15) The effective area Aef f represents the geometric area of the detector multiplied

by the detection efficiency in units of cm2_{. The P SF factor describes the}

re-sponse of the instrument to a point source. The factor Edisp takes into account

the difference between the reconstructed event energy and the true photon en-ergy. This energy dispersion effect becomes important at low enen-ergy.

Given an incoming primary γ-ray of intensity I(p, E, t) as a function of direction of the true photon p, its energy E and time t, the expected event rate with reconstructed position p′

, energy E′ and time t′ is e(p′ , E′ , t′ ) = Z R(p′ , E′ , t′ |p, E, t) × I(p, E, t) dp dE dt . (16)

A partial list of ctools programs involved in our tests is shortly described below.

15

(35)

ctobssim to simulate photons lists. It generates events that will be analyzed using our data pipelines. The simulations need a model for the astrophys-ical source and the background with the receiving instrument characteris-tics. Furthermore the program requires other parameters to describe the observation as location, time and energy boundaries.

ctselect to cut the lists of events in time, energies or positions. It represents a quick tool to reshape the starting dataset.

ctlike determinates the model free parameters (i.e. flux, spectral index, po-sition and more) analyzing binned or unbinned data. This procedure is clearly the ctools’ “workhorse” module. A significant amount of the workflows goes through the use of ctlike program that detects the input type16 _{and adapts its analysis to provide a final model}17 _{containing the}

best fitting parameters using the maximum likelihood approach. csphagen is a ctools script to extract data cubes18

from on-source and off-source regions. It provides a set of data as On-Off observation needed to perform the on/off analysis with ctlike.

cslightcrv is part of cscripts. It computes an observation lightcurve starting from an event list and using a model and ctlike for each selected time bin. It can operate in different ways, including “unbinned” and “onoff”. ctskymap is a ctools program to generate a sky map from a selected list of

events. It is fundamental to decide the pixel-degree scale and the resulting image pixel size. This program can also perform an energy cut and apply a background-subtraction method.

ctoolsprovide skymap, spectra, residual analysis and different ways to bin data over many dimensions (usually spatial coordinates, energies and time). Furthermore, the framework allows user to run binned and unbinned likelihood analysis to provide best-fit models as final result.

For unbinned data ctools uses the Poisson formula to compute the log-likelihood function: − ln L(M) = E(M) −X i ln P (p′ i, E ′ i, t ′ i|M) (17)

where P is the probability density that, given the model M , an event with instrument direction p′

, measured energy E′

and trigger time t′

occurs. E(M )

16

Many ctools programs, including ctlike, accept different input as plain event list, counts cube or observation definition XML file.

17

The model XML file is inspired from the Large Area Telescope aboard NASA’s Fermi satellite (Fermi-LAT) science tools and it is com-patible with it. More info about ctools models are provided here http://cta.irap.omp.eu/gammalib/users/user_manual/modules/model/sky/index.html.

18

Data cubes are multi-dimensional matrix filled with data binned in their specific di-mensions — typical cases have counts splitted for spatial coordinates and energy bins. In csphagenoutput the data are binned by energy dimension.

(36)

is the total number of events predicted, computed integrating the probability density over energies (the energy bounds, Ebounds), contiguous time interval (called Good Time Intervals, GTIs) and region of interest (ROI) as

E(M ) = Z GT I Z Ebounds Z ROI P (p′ , E′ , t′ |M) dp′ dE′ dt′ . (18)

For binned data ctools computes the likelihood following a Poisson distri-bution

− ln L(M) =X

i

ei(M ) − niln ei(M ) (19)

where the i data are taken from binned data. ni is the observed events in the

bin i, and the predicted number of events for model M is ei(M ) = P (p′i, E

′ i, t

′

i|M) × Ωi× ∆Ei× ∆Ti (20)

where the probability density P is multiplied by the solid angle Ωi, the energy

∆Ei and the exposure time ∆Ti.

3.2 The ctools reflection method

The ctools csphagen script can generate the on/off observation using the re-flected background algorithm; see § 2.4 for a general description of the rere-flected background method. The software will use a source region shape and a pointing distance to generate off regions that are “reflected” with respect to the point-ing direction, by placpoint-ing regions of the same source shape19 _{at the same offset}

to the pointing direction, leading to reduced systematic uncertainties in the background determination.

The csphagen reflection algorithm implementation considers the on and off regions on the circumference having as radius the distance between pointing and source region center. As shown in Figures 13a and 13b, a larger distance from the target is reflected in a larger number of background regions, and therefore in a different background scaling factor α (see equation 2).

This method is derived by the “wobble mode” pointing and uses all the possible off regions on the circumference skipping only the nearest ones to the source region. Number of regions apart, the method follows the same guideline of false source tracking mode described in § 2.5: an observation session collects on and off counts at the same time and conditions. Furthermore, we will obtain the count excess subtracting averaged background counts from the on source photons.

The reflected regions are used by csphagen to provide a fits file in OGIP20

format with the total counted photons for each energy channel selected. This off count will be used as Nof f in equation 1 to extimate the probable number

of photons from source. The background scaling factor α is also contained for

19

At the moment of writing, only circular regions are supported.

20

(37)

each energy channel. csphagen will not provide a complete on/off observation if the distance between pointing and source is not enough to compute off regions safely — the angular distance is expected to be larger than approx 0.5 degrees. In this particular condition, the program will silently create only an on-source observation.

(38)

0 1.8 3.6 5.4 7.2 9 11 13 14 16 18 35.000 34.000 33.000 32.000 31.000 30.000 -51.000 -51.500 -52.000 -52.500

(a) In this skymap the pointing declination is source dec +0.5◦_.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 87.000 86.500 86.000 85.500 85.000 84.500 84.000 83.500 83.000 82.500 24.500 24.000 23.500 23.000 22.500 22.000

(b) The telescope pointing is +1.0◦_{on RA and Dec shift with respect to source} center.

Figure 13: The reflection algorithm draws regions during the Crab simulation. The green region is on source, the red regions are off source. The number of off regions is strictly dependent on the distance between the pointing direction and the source. It is possibile to appreciate the “skipped” regions near the source to avoid spilled counts.